A surface plasmon resonance-based solution affinity assay for heparan sulfate-binding proteins

A surface plasmon resonance-based solution affinity assay is described for measuring the Kd of binding of heparin/heparan sulfate-binding proteins with a variety of ligands. The assay involves the passage of a pre-equilibrated solution of protein and ligand over a sensor chip onto which heparin has been immobilised. Heparin sensor chips prepared by four different methods, including biotin–streptavidin affinity capture and direct covalent attachment to the chip surface, were successfully used in the assay and gave similar Kd values. The assay is applicable to a wide variety of heparin/HS-binding proteins of diverse structure and function (e.g., FGF-1, FGF-2, VEGF, IL-8, MCP-2, ATIII, PF4) and to ligands of varying molecular weight and degree of sulfation (e.g., heparin, PI-88, sucrose octasulfate, naphthalene trisulfonate) and is thus well suited for the rapid screening of ligands in drug discovery applications.

A Numerical Solution Using an Adaptively Preconditioned Lanczos Method for a Class of Linear Systems Related with the Fractional Poisson Equation

This study considers the solution of a class of linear systems related with the fractional Poisson equation (FPE) (−∇2)α/2φ=g(x,y) with nonhomogeneous boundary conditions on a bounded domain. A numerical approximation to FPE is derived using a matrix representation of the Laplacian to generate a linear system of equations with its matrix A raised to the fractional power α/2. The solution of the linear system then requires the action of the matrix function f(A)=A−α/2 on a vector b. For large, sparse, and symmetric positive definite matrices, the Lanczos approximation generates f(A)b≈β0Vmf(Tm)e1. This method works well when both the analytic grade of A with respect to b and the residual for the linear system are sufficiently small. Memory constraints often require restarting the Lanczos decomposition; however this is not straightforward in the context of matrix function approximation. In this paper, we use the idea of thick-restart and adaptive preconditioning for solving linear systems to improve convergence of the Lanczos approximation. We give an error bound for the new method and illustrate its role in solving FPE. Numerical results are provided to gauge the performance of the proposed method relative to exact analytic solutions.

Fundamental solution and discrete random walk model for time-space fractional diffusion equation

In this paper, we consider a time-space fractional diffusion equation of distributed order (TSFDEDO). The TSFDEDO is obtained from the standard advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α∈(0,1], the first-order and second-order space derivatives by the Riesz fractional derivatives of orders β 1∈(0,1) and β 2∈(1,2], respectively. We derive the fundamental solution for the TSFDEDO with an initial condition (TSFDEDO-IC). The fundamental solution can be interpreted as a spatial probability density function evolving in time. We also investigate a discrete random walk model based on an explicit finite difference approximation for the TSFDEDO-IC.

Industrial design in endoscopy : the development of a tissue and organ extractor

Throughout history, developments in medicine have aimed to improve patient quality of life, and reduce the trauma associated with surgical treatment. Surgical access to internal organs and bodily structures has been traditionally via large incisions. Endoscopic surgery presents a technique for surgical access via small (1 Omm) incisions by utilising a scope and camera for visualisation of the operative site. Endoscopy presents enormous benefits for patients in terms of lower post operative discomfort, and reduced recovery and hospitalisation time. Since the first gall bladder extraction operation was performed in France in 1987, endoscopic surgery has been embraced by the international medical community. With the adoption of the new technique, new problems never previously encountered in open surgery, were revealed. One such problem is that the removal of large tissue specimens and organs is restricted by the small incision size. Instruments have been developed to address this problem however none of the devices provide a totally satisfactory solution. They have a number of critical weaknesses: -The size of the access incision has to be enlarged, thereby compromising the entire endoscopic approach to surgery. - The physical quality of the specimen extracted is very poor and is not suitable to conduct the necessary post operative pathological examinations. -The safety of both the patient and the physician is jeopardised. The problem of tissue and organ extraction at endoscopy is investigated and addressed. In addition to background information covering endoscopic surgery, this thesis describes the entire approach to the design problem, and the steps taken before arriving at the final solution. This thesis contributes to the body of knowledge associated with the development of endoscopic surgical instruments. A new product capable of extracting large tissue specimens and organs in endoscopy is the final outcome of the research.